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4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m 2 . She currently has $2025. a. Would she be willing to und

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Answer #1

Given U=m1/2

Utility in case of no gamble is given by

U(2025)=20251/2 =45 utils

a)

In case of gamble

Wealth in case of win=2025+2875=$4900

Probability of win=p=1/4

Utility in case of win=U(4900)=49001/2=70 utils

Wealth in case of loss=2025-1125=$900

Probability of loss=q=3/4

Utility in case of loss=U(900)=9001/2=30 utils

Expected utility=p*U(4900)+q*U(900)=1/4*70+3/4*30=40 utils

We can see that expected utility in case of gable is lower than utility in case of no gamble. So, Kate would not prefer gamble.

b)

In case of gamble

Wealth in case of win=2025+2599=$4624

Probability of win=p=1/3

Utility in case of win=U(4624)=46241/2=68 utils

Wealth in case of loss=2025-800=$1225

Probability of loss=q=2/3

Utility in case of loss=U(900)=12251/2=35 utils

Expected utility=p*U(4624)+q*U(1225)=1/3*68+2/3*35=46 utils

We can see that expected utility in case of gable is higher than utility in case of no gamble. So, Kate will take gamble.

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